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Find the competitive equilibrium price p and the equilibrium allocation

Find the competitive equilibrium price p and the equilibrium allocation

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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please only answer part ii

Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of good 1 and ₂ units of good 2, their utility is given by u(x₁, x2) = aln x₁ + ln x2, where a > 0 is a free parameter. (i) How does the parameter a affect the marginal rate of substitution between goods 1 and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter a increases.
Transcribed Image Text:Question 1 Consider an economy with two goods t = 1,2. Whenever an individual consumes ₁ units of good 1 and ₂ units of good 2, their utility is given by u(x₁, x2) = aln x₁ + ln x2, where a > 0 is a free parameter. (i) How does the parameter a affect the marginal rate of substitution between goods 1 and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter a increases.
Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How- ever, the parameter a is higher for consumer A than for consumer B, i.e., we have a > a³. Consumer A is endowed with 3 units of good 1, but has no endowment of good 2. Consumer B has no endowment of good 1, but has 3 units of good 2. In the remainder of this question, let p denote the price of good 1 and let the price of good 2 be normalised to 1. (ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of the parameters aª and a³. Which good is consumed in greater amount by consumer A? Which good is consumed more by agent B? Interpret your results in relation to your answer in part (i).
Transcribed Image Text:Consider an exchange economy with two consumers, A and B, whose utilities are given as above. How- ever, the parameter a is higher for consumer A than for consumer B, i.e., we have a > a³. Consumer A is endowed with 3 units of good 1, but has no endowment of good 2. Consumer B has no endowment of good 1, but has 3 units of good 2. In the remainder of this question, let p denote the price of good 1 and let the price of good 2 be normalised to 1. (ii) Find the competitive equilibrium price p and the equilibrium allocation expressed as a function of the parameters aª and a³. Which good is consumed in greater amount by consumer A? Which good is consumed more by agent B? Interpret your results in relation to your answer in part (i).
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